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I don't understand this "trapped ion (qubit implemented by the internal state of trapped ions)"

One qubit implemented by the internal state of trapped ions (plural)?

"Consider an ion trap. The ions represent qubits by using one electronic state as a |0⟩ and another as a |1⟩"

What are these ions states physically?

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    $\begingroup$ One trapped ion implements one qubit; looks like the question is about using plurals in English. $\endgroup$ – kludg Nov 29 '19 at 8:58
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The ion states are the different energy states of the ion. These different energy states can be denoted with the total spin of the ion and the phonon levels of the ion.

If we look at a Helium atom which has two electrons the total spin can be S = 0 if the electrons are in the following spin state: $$ \frac{1}{\sqrt{2}}(\uparrow \downarrow-\downarrow \uparrow) $$ or the total spin can be S=1 if the electrons are in one of the following three states $$ \downarrow \downarrow $$ $$ \frac{1}{\sqrt{2}}(\uparrow \downarrow+\downarrow \uparrow) $$ $$ \uparrow \uparrow $$ The phonon levels represent motional states of the atom.

Often two ion energy states with a different total spin and 0 phonons are chosen as the qubit $|0\rangle$ and $|1\rangle$ state.

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